Strapdown inertial navigation systems are frequently used in missiles and aircraft. Physically isolated and stabilized apparatus, such as a gimballed platform that is physically angularly stabilized relative to the local vertical direction, would require precise and mechanically complex angle positioning apparatus.
A state-of-the-art strapdown inertial navigation system has three angle sensors or gyros and three accelerometers rigidly attached to a supporting vehicle. The angle sensors are each positioned and oriented to sense angular displacement about one of three defined orthogonal axes attached to the vehicle body, and therefore known as, "body axes." The accelerometers are each positioned and oriented in a fixed direction relative to the vehicle, to sense velocity changes (incremental velocities) along different ones of the three defined orthogonal axes.
In a strapped down system the accelerometer axes are not angularly stabilized. Because the accelerometers are constantly changing direction relative to gravity, navigation velocities cannot be computed by directly integrating the accelerometer signals. Instead, a stable computational frame or analytic navigational coordinate system is continually generated. The output signals from the angle sensors are used by an attitude integration apparatus to calculate the directions of local vertical, together with two other axes orthogonal to the local vertical direction. Sensed angle changes and accelerations (incremental velocities) are continually rotated through the calculated angles from the vehicle body axes to the calculated navigation axes.
Angle signals from the angle sensors are used to update the computer-stored angular position and incremental velocity data for both the angle sensors and accelerometers relative to the stable analytic navigational coordinate system. The angle sensors and accelerometers have fixed relative directions in the body axes system An angular transformation matrix of directions cosines is computed in an attitude integration apparatus. The accelerometer signals, which are incremental changes in velocity, in the strapped down coordinate system are converted in a coordinate transformation computer from that system into corresponding signals in the stabilized navigational coordinate system. After transformation into the navigational coordinate system, the incremental velocity signals are integrated or summed to form updated velocity signals.
The angle sensor and accelerometer signals are sampled, and the sampled signals are delivered to a computer which is pre-programmed to accept the signals and to calculate both velocities along and angles about the three axes in the stabilized navigation coordinate system. The stabilized coordinate system is designated herein as the "navigation platform,." and its axes are designated the "navigation axes." An angle transformation matrix is created in the attitude integration apparatus to transform vector body-coordinate signals(for example, incremental velocity component signals) from the body axes of the instruments to the navigation axes. The transformed signals are used to calculate and create signals that are measures of the local geographical position of the aircraft and the direction of the local gravity. The transformation matrix also yields signals that are measures of the angular orientation of the supporting vehicle relative to the navigation axes.
The data used to compute the transformation matrix is sampled at finite periodic intervals, causing the bandwidth of the signals to be limited. When the instruments sense vibrations that occur at frequencies above or near the upper limit of the bandwidth of the transformation, where the response is poor, rectification errors occur in the calculated incremental velocity signals, and the navigation system signals are degraded. The rectification errors producing such degrading are called sculling errors.
A sculling error for a first strapped down axis is caused by a periodic angular displacement about a second axis perpendicular to that axis, multiplied by the periodic acceleration along a third axis perpendicular to the first and second axes.
To reduce the sculling error in strapdown systems, the sampling rate of the instrument signals may be increased. The upper limit of the sampling rate is set by the capabilities of the computer. An increase in sampling rate in a fast computer would likely increase the number of its calculations. The faster the computer, the greater its initial cost. The larger number of calculations might also require a prohibitively sophisticated computer with large power demand.
Instead of increasing the iteration rate for the transformation of incremental velocity from one coordinate system to the other, one might use a first order sculling error correcting algorithm which has the effect of emulating a faster transformation rate.
The "order" of the sculling error correcting algorithm refers to the number of sampling intervals used in each calculation of the algorithm.
One could use both a faster sampling and the first order correction to improve further the transformation of incremental velocity from the strapped down coordinates into the navigation coordinates.